2015 Fiscal Year Final Research Report
Semigroup-theoretic study of identification problem in evolution equations
| Project/Area Number |
25400182
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
Yokota Tomomi 東京理科大学, 理学部第一部, 准教授 (60349826)
Yoshii Kentarou 東京理科大学, 理学部第一部, 助教 (00632449)
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Keywords | 発展方程式 / 同定問題 / 作用素半群理論 / 角型極大増大作用素 / 双対性写像 / フレシェ微分 / 陰関数定理 / 連鎖律 |
|---|
| Outline of Final Research Achievements |
We are concerned with linear evolution equations of parabolic type (d/dt)u(t)+νAu(t) = 0 (0<t<T), where A-ω (ω>0) is an m-sectorial operator in a Banach space X and the coefficient ν＞０ is a parameter. The theory of operator-semi-groups says that under the setting the unique solvability of the equation (with coefficient) is guaranteed. In fact, given an initial value u(0) = x in X, a unique solution of the initial-value problem can be written as u(t) = exp(-tνA)x, where {exp(-tνA)} is the analytic contraction semigroup generated by -νA. In identification problem we specify the coefficient ν by some additional information besides the unique existence of solutions. Measuring the norm ρ=||exp(-TνA)x|| of the final value u(T) as an additional information, we could have determined a unique implicit function ν=ν(x, ρ) which depends on initial-value x and norm ρ locally Lipschitz continuously.
|
| Free Research Field |
数物系科学
|
